Theorems · Theorem · general topology
Isometry.uniformContinuous
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → UniformContinuous fAn isometry from a metric space is a uniform continuous map
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- UniformContinuousstatement · cited by 410
- Isometrystatement and proof · cited by 230
- LipschitzWith.uniformContinuousproof · cited by 33
- Isometry.lipschitzproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Isometry.isUniformInducingproof · cited by 10
- Isometry.completion_extensionproof · cited by 4
- Isometry.mapRingHom_coeproof · cited by 2